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Arithmetic Brownian motion subordinated by tempered stable and inverse tempered stable processes

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  • Wyłomańska, Agnieszka

Abstract

In the last decade the subordinated processes have become popular and have found many practical applications. Therefore in this paper we examine two processes related to time-changed (subordinated) classical Brownian motion with drift (called arithmetic Brownian motion). The first one, so called normal tempered stable, is related to the tempered stable subordinator, while the second one–to the inverse tempered stable process. We compare the main properties (such as probability density functions, Laplace transforms, ensemble averaged mean squared displacements) of such two subordinated processes and propose the parameters’ estimation procedures. Moreover we calibrate the analyzed systems to real data related to indoor air quality.

Suggested Citation

  • Wyłomańska, Agnieszka, 2012. "Arithmetic Brownian motion subordinated by tempered stable and inverse tempered stable processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5685-5696.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:22:p:5685-5696
    DOI: 10.1016/j.physa.2012.05.072
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    References listed on IDEAS

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    1. Burnecki, Krzysztof & Misiorek, Adam & Weron, Rafal, 2010. "Loss Distributions," MPRA Paper 22163, University Library of Munich, Germany.
    2. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
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    3. Jabłońska-Sabuka, Matylda & Teuerle, Marek & Wyłomańska, Agnieszka, 2017. "Bivariate sub-Gaussian model for stock index returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 628-637.

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